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log(x^5,3)
The derivative of the function/ log(x^5,3)

Derivative of log(x^5,3)

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   / 53\
   | --|
   | 10|
log\x  /
log⁡(x5310)\log{\left(x^{\frac{53}{10}} \right)} 
  /   / 53\\
  |   | --||
d |   | 10||
--\log\x  //
dx
ddxlog⁡(x5310)\frac{d}{d x} \log{\left(x^{\frac{53}{10}} \right)}
Transform
Detail solution

  1. Let u=x5310u = x^{\frac{53}{10}}.

  2. The derivative of log⁡(u)\log{\left(u \right)} is 1u\frac{1}{u}.

  3. Then, apply the chain rule. Multiply by ddxx5310\frac{d}{d x} x^{\frac{53}{10}}:

    1. Apply the power rule: x5310x^{\frac{53}{10}} goes to 53x431010\frac{53 x^{\frac{43}{10}}}{10}

    The result of the chain rule is:

    5310x\frac{53}{10 x}

The answer is:

5310x\frac{53}{10 x}

The graph
02468-8-6-4-2-1010-100100
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
 53 
----
10*x
5310x\frac{53}{10 x}
Simplify
The second derivative [src] 
 -53 
-----
    2
10*x
−5310x2- \frac{53}{10 x^{2}}
Simplify
The third derivative [src] 
 53 
----
   3
5*x
535x3\frac{53}{5 x^{3}}
Simplify
The graph
Derivative of log(x^5,3)
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